Why is it important to apply transformation to an objects data?
Short answer: it depends.

Applying transformation can be important but it mostly comes down to what you do intend to do with the objects.

Looking at this from a simplistic viewpoint, ideally it wouldn't matter and everything would work just fine even when scaled/rotated.

A good rule of thumb is:


  Apply rotation and scale to your models unless you have a reason not to.


Transformation is split up into translation/rotation/scale, generalizing on Blender's support:


rotated objects (well supported)
translated objects (well supported)
scaled objects (well supported)
non-uniform scaled objects
negative scaled objects


The last 2 can cause issues with modifiers, constraints and some tools. Even though for basic operations it works fine, there's rarely a good reason to have negative scale.

Considerations:


Most modifiers are applied before scale. So the effect of a bevel or solidify could be squashed with non-uniform scale. Armature and hook modifiers are an exception to this rule.
Negative scale will flip the object's normals (when an odd number of axes is flipped).
Most edit mode tools such as smooth-subdivide won't take non-uniform scale into account.
Rotation and scale can cause problems with armatures, especially when exporting to different formats.
Rigid body physics doesn't support scaled objects well (this could be seen as a bug, nevertheless as it stands it's not working well).
Scale applied after parenting will be applied to children, if you have complex parent/child setups - it's less trouble if you only scale objects when necessary.
Extreme scale values &gt;1000.0 or &lt;0.0001 (a large object scaled down or a small object scaled up) can cause floating point math precision issues when in edit mode, also for other calculations.


Areas scaled/transformed objects are fine:


Static scenery (maybe you want to have different sized rocks). Objects which don't move or interact with other objects via modifiers, constraints etc.
When it's intentional - an object stretches (animate scale with a bouncing ball).